A Remark on the Use of a Weight Matrix in the Linear Model of Coregionalization

Samuel D. Oman, Bella Vakulenko-Lagun

Research output: Contribution to journalArticlepeer-review


The linear model of coregionalization (LMC) is generally fit to multivariate geostatistical data by minimizing a least-squares criterion. It is commonly believed that weighting the criterion by inverse variances will reduce the influence of those variables with large variance. We point out that this need not be so, and that in some cases the weights will have no effect whatsoever on the estimated sill matrices. When there is an effect, it is due not to a reduction of these variables' influence, but rather due to a lack of invariance of the minimization problem; moreover, sometimes the influence may actually increase. The correct way to reduce influence is to fit the LMC after standardizing the variables to have unit variance.

Original languageEnglish
Pages (from-to)505-512
Number of pages8
JournalMathematical Geosciences
Issue number4
StatePublished - May 2012
Externally publishedYes


  • Factor analysis
  • Invariance
  • Linear model of coregionalization
  • Principal components
  • Standardization

ASJC Scopus subject areas

  • Mathematics (miscellaneous)
  • General Earth and Planetary Sciences


Dive into the research topics of 'A Remark on the Use of a Weight Matrix in the Linear Model of Coregionalization'. Together they form a unique fingerprint.

Cite this